A mattress manufacturer produces mattresses in 5 locations in the North America. The company isplanning a new production plant which will supply box springs to all 5 mattress plants. The mattressplants have been located on a coordinate system as follows:Mattress PlantCoordinates (X,Y)A7,2В4,55,4D6,1E8,3Suppose shipments of box springs to each plant per week were the following: plant A 200 units; plant B400 units; plant C 300 units; plant D 400 units; plant E 100 units. Which of the following is the closestto the optimal location for the box spring plant?O A. 7.7,4.3O B. 5.5,3.1O C. 4.3,7.7O D. 3.1,4.3OE. 3.1,5.5

Optimal location: The optimal location is the location that will be nearest to all 5 plants and…

Answered: A mattress manufacturer produces…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 100P

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Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table: Potential Locationsfor Substations Areas Covered A 1, 5, 7 B 1, 2, 5, 7 C 1, 3, 5 D 2, 4, 5 E 3, 4, 6 F 4, 5, 6 G 1, 5, 6, 7 Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas.
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A concrete company transports concrete from their three plants in Nyanyano.- town, Feteh. -town and Tuba.- town to their three construction sites in Ofaakor.- site, Papaase.- site and Krodua. -site. The supply capacities of the three plants, the demand requirements at the three sites, and the transportation costs per ton are as follows: Construction Site Plant O.- site P.- site K. -site Supply(tons) N. town GHs 8 GHs 5 GHs 6 GHs 120 F. town 15 10 12 80 T. town 3 9 10 80 Demand(tons) 150 70 100 280 XXXa) Establish the decision variables for this transportation problem. XXXb) Develop a network graph showing all costs and decision variables. c) i. Formulate the mathematical model that will be used to solve the problem on a computer ii. Fine the initial feasible solution using the Northwest Corner Rule and the total cost. PLEASE ANSWER ONLY C i and C ii PART OF THE QUESTION.

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